Theorems · Theorem · group theory
neg_inj
∀ {G : Type u_3} [inst : InvolutiveNeg G] {a b : G}, -a = -b ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- InvolutiveNeg
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- InvolutiveNegstatement and proof · cited by 151
- neg_injectiveproof · cited by 35
Cited by85
Results whose statement or proof uses this declaration.
- mul_zsmul'proof · cited by 16
- neg_add_eq_zeroproof · cited by 14
- HasSum.nat_add_negproof · cited by 10
- Int.ceil_add_intCastproof · cited by 8
- Function.Periodic.intervalIntegral_add_eqproof · cited by 7
- ZLattice.rankproof · cited by 5
- Orientation.oangle_add_right_smul_rotation_pi_div_twoproof · cited by 4
- WeierstrassCurve.Affine.addPolynomial_slopeproof · cited by 3
- AddSemiconjBy.neg_neg_symm_iffproof · cited by 3
- Polynomial.cyclotomic_coeff_zeroproof · cited by 3
- RCLike.im_eq_conj_subproof · cited by 3
- CategoryTheory.Pretriangulated.complete_distinguished_triangle_morphism₁proof · cited by 3